Re: [Phys-L] [SPAM] Re: form of Newtons 2nd law

[John Denker <jsd@av8n.com>]

On 07/26/2012 06:01 PM, Anthony Lapinski wrote:
> I like the a = F/m form since an acceleration results from a net force.
> It's just easier to write F = ma (no fraction>) as N2L. Similarly, I write
> (derive) Ohm's law as I = V/R -- a current results from a potential
> difference. Again, it's easier to write V = IR.

I wouldn't have said that.

The word "results" can have two meanings, both of which misrepresent 
the meaning of the equation.

  a) The true meaning of the equation a = F/m is that the acceleration
   *equals* the quotient of force over mass.

  b) It is not correct to say that the acceleration must be 
   /calculated from/ force over mass.  Sometimes it is calculated that
   way, and sometimes it isn't.

  c) It is not correct to say that the acceleration is /caused/ by the
   force and/or resisted by the mass.

As a specific familiar example:  A laboratory centrifuge has a definite
radius and typically operates at a definite rotational speed.  Therefore
you know the acceleration.  From that you can calculate the force.

Similarly, one of the first serious R&D contracts I ever signed was to
build a motion-control system for a Hollywood special effects company.
The thing was driven by stepper motors, which for all intents and purposes
dictated the position as a function of time.  When we designed the trajectories,
we calculated the velocity, acceleration, and jerk.  We calculated the force
by multiplying mass times acceleration.

Other examples abound.

Don't tell me that acceleration has to be calculated in terms of force
over mass.  It just isn't true.  Yes, you can add forces on one side of
the equation, but you can just as well add accelerations on the other
side of the equation.  Acceleration is a vector. The vector-space axioms
guarantee you can add them.  Maybe all the homework problems in the
textbook you are using assume that we need to calculate the acceleration
based on known forces, but this just reflects the authors' lack of 
experience, lack of erudition, and lack of imagination.

By all that's holy, an equation expresses an /equivalence relation/.  As
such, it is symmetric, reflexive, and transitive.
  http://en.wikipedia.org/wiki/Equivalence_relation#Definition

Any assertion that A "results" from B, is "calculated from" B, or is "caused"
by B is not an equivalence relation, because it is not symmetric.

Almost all the basic laws of physics are equations.  They are equivalence
relations.  They are symmetric.  The F=ma law says you can't have F without
ma ... and vice versa.  It means exactly the same thing as ma=F, and for
all nonzero m it means the same as a=F/m.
 
For more on this, see
  http://www.av8n.com/physics/causation.htm